Do hawks commonly drown their prey?

I was recently shown a video of a red-tailed hawk drowning a duck in a pond near my house. The duck thrashed for quite a while after the hawk landed on it and afterward the hawk tried to fly away with it but I don’t know if it succeeded. Since then I was told of another incident of a hawk apparently keeping a squirrel underwater on a pool cover before leaving with it. Is this common?

It’s extremely rare for any raptor that I know of. I can’t say I can recall hearing of other cases offhand. Hawks normally kill their prey by stunning them or with their beaks or talons.

Based on a decent amount of observation both during falconry and in the wild, I’d agree that this has to be extremely rare.

I’d speculate that the two cases mentioned in the OP may be coincidental: hawk happens to brings prey to earth near water.

In the first instance, the hawk appeared to just land on the duck and push the duck underwater from the beginning and sit on it. Do other birds do it and it could have learned from them?

Do you mean other species? I am not aware of any species of bird that routinely kills air-breathing prey by drowning it.

Whenever I learn of special techniques some species use–for whatever, but often it’s for catching prey–like margays imitating monkeys, I always wonder how the species figured out that particular trick. Did they teach each other, or what?

Several websites say the Cooper’s Hawk may drown its prey.
From Bird Eden.

From Whatbird.com

There are a few anecdotal reports in the literature, but the behavior is rare enough that individual reports are considered publishable. It’s not a typical hunting behavior even for Cooper’s.

Interestingly (to me). just yesterday I saw an Bald Eagle grab a duck and fly away with it right in front of our house. (It took several passes to get a good grab). No attempt to drown it. Quite a commotion, as you can imagine.